There are infinite black and white dots on a plane. Prove that the distance between one black dot and one white dot is one unit.

A Russian gangster kidnaps you. He puts two bullets in consecutive order in an empty six-round revolver, spins it, points it at your head and shoots. Click. You're still alive. He then asks you, do you want me to spin it again and fire or pull the trigger again. For each option, what is the probability that you'll be shot?

How much would it cost to implement a product improvement for the entire US?

Why wouldn't I hire you?

A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a white or black hat on each dwarf. No dwarf can see their own hat. The giant tells all the dwarfs that he will ask each dwarf, starting with the tallest, for the color of his hat. If the dwarf answers incorrectly, the giant will kill the dwarf. Each dwarf can hear the previous answers, but cannot hear when a dwarf is killed. The dwarves are given an opportunity to collude before the hats are distributed. What strategy should be used to kill the fewest dwarfs, and what is the minimum number of dwarfs that can be saved with this strategy?